Question

Use the permutation or combination rule. A basketball coach must pick 5 players from a roster of 12 to start a game. In how many ways can he choose his staring 5 players assuming that all players have equal ability?

Name: Problem 48, Chapter 11: Intermediate Algebra
Uploaded: 2020-06-27T11:25:02-08:00
Duration: 1 min
Channel: Ankit Gupta
Description: Use the permutation or combination rule. A basketball coach must pick 5 players from a roster of 12 to start a game. In how many ways can he choose his staring 5 players assuming that all players have equal ability?

   Use the permutation or combination rule.
A basketball coach must pick 5 players from a roster of 12 to start a game. In how many ways can he choose his staring 5 players assuming that all players have equal ability?

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 11, Problem 48

Instant Answer

Solved by Expert Ankit Gupta

06/27/2020

Step 1

The order of selection does not matter here, so we use the combination formula. The combination formula is given by: \[C(n, k) = \frac{n!}{k!(n-k)!}\] where \(n\) is the total number of items, \(k\) is the number of items to choose, and \(n!\) (read as "n Show more…

Show all steps

Thanks for your feedback!

Use the permutation or combination rule. A basketball coach must pick 5 players from a roster of 12 to start a game. In how many ways can he choose his staring 5 players assuming that all players have equal ability?

Play audio

Feedback

Ankit Gupta and 79 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Combination

A combination is a method for selecting items from a larger set where the order of selection does not matter. In problems like choosing team members or committee members, combinations are used because the group is defined solely by which items are chosen, not by the order in which they are selected.

Binomial Coefficient

The binomial coefficient, often notated as nCk or (n choose k), gives the number of ways to choose k items from a set of n items without considering the order of selection. It is calculated using factorials, solidifying its role in combinatorial problems where the arrangement is irrelevant.

Please give Ace some feedback